Abstract
As a recurrent problem in numerical analysis and computational science, eigenvector and eigenvalue determination usually employs high-performance linear algebra libraries. This paper explores the implementation of high-performance routines for the solution of multiple large Hermitian eigenvector and eigenvalue systems on a Graphics Processing Unit (GPU). We report a performance increase of up to two orders of magnitude over the original \(\textsc{Eispack} {}\) routines with a NVIDIA Tesla C2050 GPU, providing an effective order of magnitude increase in unit cell size or simulated resolution for Inelastic Neutron Scattering (INS) modelling from atomistic simulations.
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References
Bethel, E., van Rosendale, J., Southard, D., Gaither, K., Childs, H., Brugger, E., Ahern, S.: Visualization at Supercomputing Centers: The Tale of Little Big Iron and the Three Skinny Guys. IEEE Computer Graphics and Applications 31(1), 90–95 (2011)
Cline, A.K., Meyering, J.: Converting eispack to run efficiently on a vector processor. Tech. rep., Pleasant Valley Software, Austin, Texas (1991)
Dongarra, J.J., Duff, I.S., Sorensen, D.C., van der Vorst, H.A.: Numerical linear algebra for high-performance computers, 2nd edn. SIAM (1998)
Du, P., Weber, R., Luszczek, P., Tomov, S., Peterson, G., Dongarra, J.: From CUDA to OpenCL: Towards a performance-portable solution for multi-platform GPU programming. Parallel Computing (2011) (in Press), doi:10.1016/j.parco.2011.10.002
Feldman, S.: A Fortran to C converter. ACM SIGPLAN Fortran Forum 9(2), 21–22 (1990)
Gale, J.D., Rohl, A.L.: The general utility lattice program (GULP). Molecular Simulation 29(5), 291–341 (2003)
Garba, M., González-Vélez, H.: Towards ad-hoc GPU acceleration of parallel eigensystem computations. In: ECMS 2011: 25th European Conference on Modelling and Simulation. ECMS, Krakow (June 2011)
Garba, M., González-Vélez, H., Roach, D.: Parallel computational modelling of inelastic neutron scattering in multi-node and multi-core architectures. In: 11th IEEE Int. Conf. on High Performance Computing and Communications, pp. 509–514. IEEE, Melbourne (2010)
Govindaraju, N.K., Larsen, S., Gray, J., Manocha, D.: A memory model for scientific algorithms on graphics processors. In: SC 2006: ACM/IEEE Conf. on Supercomputing, p. 6. IEEE, Tampa (2006)
Kirk, D., Wen-mei, W.: Programming massively parallel processors: A Hands-on approach. Morgan Kaufmann Publishers Inc., San Francisco (2010)
Lee, S., Min, S.J., Eigenmann, R.: Openmp to gpgpu: a compiler framework for automatic translation and optimization. SIGPLAN Not. 44, 101–110 (2009)
Nickolls, J., Buck, I., Garland, M., Skadron, K.: Scalable parallel programming with CUDA. Queue 6(2), 40–53 (2008)
Nvidia Corporation: NVIDIA CUDA C Programming Best Practices Guide. Manual Version 2.3, NVIDIA (2009), http://developer.nvidia.com/ (last accessed: February 1, 2011)
Roach, D., Ross, K., Gale, J.D.: The application of coherent inelastic neutron scattering to the study of polycrystalline materials (2012) (in Preparation)
Roach, D.L., Gale, J., Ross, D.: Scatter: A New Inelastic Neutron Scattering Simulation Subroutine for GULP. Neutron News 18(3), 21–23 (2007)
Smith, B.T., Boyle, J.M., Dongarra, J., Garbow, B.S., Ikebe, Y., Klema, V.C., Moler, C.B.: Matrix Eigensystem Routines - EISPACK Guide, 2nd edn. LNCS, vol. 6. Springer, Heidelberg (1976)
Tomov, S., Dongarra, J., Baboulin, M.: Towards dense linear algebra for hybrid GPU accelerated manycore systems. Parallel Computing 36(5-6), 232–240 (2010)
Tomov, S., Nath, R., Ltaief, H., Dongarra, J.: Dense linear algebra solvers for multicore with GPU accelerators. In: IPDPS 2010 Workshops, pp. 1–8. IEEE, Atlanta (2010)
Ueng, S.-Z., Lathara, M., Baghsorkhi, S.S., Hwu, W.-m.W.: CUDA-lite: Reducing GPU programming complexity. In: Amaral, J.N. (ed.) LCPC 2008. LNCS, vol. 5335, pp. 1–15. Springer, Heidelberg (2008)
Vázquez, F., Fernández, J.J., Garzón, E.M.: A new approach for sparse matrix vector product on NVIDIA GPUs. Concurrency and Computation: Practice and Experience 23(8), 815–826 (2011)
Wilkinson, J., Reinsch, C.: Linear Algebra. Handbook for Automatic Computation, vol. 2. Springer (1971)
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Garba, M.T., González–Vélez, H., Roach, D.L. (2013). GPU Acceleration for Hermitian Eigensystems. In: Nguyen, NT., Kołodziej, J., Burczyński, T., Biba, M. (eds) Transactions on Computational Collective Intelligence X. Lecture Notes in Computer Science, vol 7776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38496-7_10
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DOI: https://doi.org/10.1007/978-3-642-38496-7_10
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